Relativity of judgements about sound amplitude and the asymmetry of the same-different ROC

The problem of deciding whether two things are the same or different in magnitude can be solved by judging one magnitude relative to the other, or by making absolute judgements about the magnitude of each. The shape of the resulting receiver operating characteristic depends on which solution is adopted. In order to obtain empirical receiver operating characteristics, we therefore had subjects rate their confidence that two tone amplitudes were the same or different. Four subjects each made 500 ratings of three differences in amplitude. The asymmetry in the obtained characteristics indicated that subjects made relative rather than absolute judgements of the amplitudes, despite the fact that making absolute judgements would lead to better performance on the task.